MCQs – Ch # 9: F.Sc Part 1
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Text Book of Algebra and Trigonometry Class XI
Merging man and maths
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Fundamentals of Trigonometry
1.
a)
b)
c)
d)
e)
2.
Angle
Radian
Degree
Minute
Second
1 rad
1’
1”
1o
None of these
1rt. angle = __________
a)
b)
c)
d)
e)
6.
1 radian
1 degree
1 angstrom
1 minute
None of these
8.
90o
180o
270o
190o
None of these
The 60th part of one degree is called one
1 degree
1 radian
1 rt. angle
All of these
None of these
The circumference of a circle r is
considered as __________
a)
b)
c)
d)
e)
9.
centimeter
radian
degree
minute
none of these
Measure of the central angle of an are of a
circle whose length is equal to the radius
of the circle is known as _________
a)
b)
c)
d)
e)
2π r
πr
3π r
4π r
None of these
1 radian = __________
a) 57°17 ′45′′
b) 47o
c) 37o
d) 38o
e) None of these
One degree is denoted by __________
a)
b)
c)
d)
e)
5.
7.
The union of two non-collinear rays which
have a common endpoint is called the …..
a)
b)
c)
d)
e)
4.
Plane Geometry
Spherical Trigonometry
Plane Trigonometry
Analytical Geometry
None of these
If a circle is divided into 360 parts, then
the angle subtended by each part at the
center of the circle is called __________
a)
b)
c)
d)
e)
3.
a)
b)
c)
d)
e)
Direction of Qibla is found by using ….
10.
1o = _________
a) 60 ′
b) 60′′
c) 3600 ′
d) 360 ′
e) None of these
MCQs – Ch # 9: F.Sc Part 1
11.
In the given figure if C is the center of the
circle, then angle θ is ________
2
16.
a
a)
b)
c)
d)
e)
12.
14.
15.
c
2a
a+b
a+b+c
2π - a
2b – 2c
17.
An arc PQ is subtends and angle 60o at the
center of a circle of radius 1 cm. The
length PQ is ________
a) 60 cm
b) 30 cm
c) π cm
6
π
d)
cm
3
e) π
cm
18
1 rad
1′
1′′
1
None of these
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π
6
, Cosθ is ___________
1
2
1
2
3
c)
2
d) −
e)
18.
3
2
2
2
In the given figure the angle θ is ……..
a
θ
b
c
a) 2π − a
b) 2π − (a + b)
c) 2π − (a + b + c)
d) a + b + c
e) 2d – 2b
19.
1′ = ………….
a)
b)
c)
d)
e)
One second is denoted by _______
a)
b)
c)
d)
e)
30o
60o
90o
220o
None of these
b) −
centimeter
radian
degree
minute
second
180o = ________
a) π radian
b) 2 π radian
c) π
2
d) 3π
4
e) None of these
= __________
If θ =
a)
The 60th part of one minute is called one ...
a)
b)
c)
d)
e)
13.
θ
4
a)
b)
c)
d)
e)
C
b
π
20.
60o
60′′
3600′′
3600o
None of these
What is the length of an arc of a circle of
radius 5cm, whose central angle is of 140o
a) 2.443 radians
b) 1.443 radians
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MCQs – Ch # 9: F.Sc Part 1
3
c) 0.443 radians
d) 2 radians
e) None of these
21.
25.
D
A
a)
b)
c)
d)
e)
B
a
θ
22.
23.
B
C
26.
< BDC = θ
π −θ
2π − θ
2π + θ
<B
For a right angled triangle ABC as shown
in the figure, we have Co sec θ = _______
B
a
c
Two right angles are the angle of measure
a)
b)
c)
d)
e)
12
28
32
96
192
182
c
θ
B
a)
b)
c)
d)
e)
C
16
In the given figure the angle a + b + c is
b
In the figure the area of triangle ABC is
A
180 ′′
180 ′
60o
90o
180o
a) c
b) c
θ
C
b
a
b
c) b
c
d) + c
−c
e) None of these
For a right angled triangle ABC as shown
in the figure we have Sin θ = _______
B
27.
a
c
A
a) a
b) c
c) c
θ
b
c
a
d) b
c
e) None of these
24.
Four right angles are the angle of measure
a)
b)
c)
d)
e)
a)
b)
c)
d)
e)
C
b
90o
180o
270o
360o
360 ′
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The system of measurement in which the
angle is measured in degrees, and its
subunits, minutes and seconds is called
28.
Circular system
Sexagesimal system
MKS system
CGS system
None of these
Cotθ = ____________
Sinθ
Cosθ
Cosθ
b)
Sinθ
1
c)
Sinθ
1
d)
Cosθ
e) None of these
a)
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MCQs – Ch # 9: F.Sc Part 1
29.
4
In the figure the surface area (shaded) of
right circular cylinder is
33.
a)
b)
c)
d)
e)
30.
a)
b)
c)
d)
e)
_________________
h
_________________
_________________ r
2π r 2 + 2π rh
2π r + π r 2 h
2π r 2
π rh
2π rh
The system of measurement in which the
angle is measured in radians is called …..
16 40 ′38′′ =
140o
17o
16o
60038′
60038′′
34.
Sin 2θ + Cos 2θ = …., for all values of θ .
a) 1
b) 0
c) 1 + Tan 2θ
d) – 1
e) None of these
35.
In the figure the length of AB is
C
a)
b)
c)
d)
e)
31.
Circular system
Sexagesimal system
MKS system
CGS system
None of these
45
A
Secθ = __________
Sinθ
Cosθ
Cosθ
b)
Cosθ
1
c)
Sinθ
1
d)
Cosθ
e) None of these
a)
b)
c)
d)
e)
a)
32.
36.
37.
A
B
D
7
6+ 2
6+2 2
12
13
16o = ________
a)
b)
c)
d)
e)
In the figure, the shaded area is given by
6
0
960o
960 ′
57600 ′
60038′
60038′′
In the figure the angle A is (AB = AC = X)
A
X
B
X
C
a) 25π / 4 − 6
b) 5π − 6
c) 25 / 4π
d) 6
e) 7π
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B
a)
b)
c)
d)
e)
X
C
50o
60o
90o
120o
180o
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MCQs – Ch # 9: F.Sc Part 1
38.
5
Two right angles are equal to
44.
The central angle of an arc of a circle
whose length is equal to the radius of the
circle is called the
a) 180 ′
b) 180 ′′
c) 648000 ′
d) 10800 ′′
e) 10800 ′
39.
40.
41.
42.
a)
b)
c)
d)
e)
The associated angle of 280o is
a) 100o
b) 10o
c) 80o
d) – 80o
e) 190o
A radian is the measure of the central
angle of an arc of a circle whose length is
equal to the
a) half of radius of the circle
b) diameter of the circle
c) radius of the circle
d) one third of radius of the circle
e) none of these
c
In the ∆ ABC the angle γ is
b
45.
Cot 180o = _________
a) 1
b) O
c) – 1
d) ∞
e) – 11
degree
radian
minute
second
none of these
<
<
o
a)
b)
c)
d)
e)
30
45o
45o
90o
120o
a)
b)
c)
d)
e)
Cosec 180o =________?
1
0
-1
∞
2 −1
46.
Sec 180o = _________
a)
b)
c)
d)
e)
47.
1
0
–1
∞
None of these
if r is the radius, m < AOB =
A
r
O
B
43.
In the ∆ABC the angle α is
B
2a
a
o
A
a)
b)
c)
d)
e)
30
C
30o
45o
60o
90o
180o
Written by NAUMAN IDREES ([email protected])
a)
b)
c)
d)
e)
1 radian
1 degree
1 minute
1 second
None of these
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MCQs – Ch # 9: F.Sc Part 1
6
In the figure the angle α is
48.
a)
b)
c)
d)
e)
45o
60o
75o
90o
– 90o
a)
b)
c)
d)
e)
One minute is denoted by
1rad
1′
1′′
1o
None of these
a)
b)
c)
d)
e)
Cos 270o =___?
1
0
-1
∞
0–2
49.
50.
53 1o =
a) 1 radian
b) 0.01745 radian
c) 0.5 radian
d) 2.5 radian
e) 1.01745 radian
54 Tan 30o = ______?
a) 1
3
b) 3
2
c) 1
2
d) 1
2
1
e) −
2
55 If an arc of length l of circle of radius r
subtends an angle θ radian at the center, then l =
1
a)
rθ
r
b)
c)
θ
θ
r
d) rθ
e) None of these
51. The area of the shaded portion in the figure is
56
C
D
In the figure the angle α is
A
N
L
O
2
B
C
M
A
2
a)
b)
c)
d)
e)
4 −π
4 − 2π
4π
4
4π - 2
a)
b)
c)
d)
e)
Tan 270o = _______?
1
0
-1
∞
π −2
52
a)
b)
c)
d)
e)
B
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57
60o
120o
180o
240o
290o
In the first quadrant Sinθ is _________
a)
b)
c)
d)
e)
positive
negative
both
not defined
none of these
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MCQs – Ch # 9: F.Sc Part 1
58
7
In the figure the length of LM is
63.
A
y
y
y
X
B
a)
b)
c)
d)
e)
a) 1
ϕ
M
L
b) 1
y
2x
C
c) r
d) ϕ
x
2x
3x
4x
8π
e) r
64.
 180 
Convert 
 to radians
 π 
a) 0.94 radians
b) 1 radians
c) 3.97 radians
d) 4.57 radians
e) 3.54 radians
59.
1o = …………
a)
b)
π
180
180
π
radians
1
radians
180π
d) 180π radians
e) π radians
c)
66.
a) π
b) π
c) π
2
4
a)
b)
c)
d)
e)
radians
24.32o
24.97o
4.96o
1.97o
23.42o
360o
335o
270o
225o
125o
9.47 radians
1.19 radians
1.5 radians
2.5 radians
None of these
150o =
6
radians
radians
3
c) π radians
4
d) 180π radians
e) π radians
radians
Convert radian measure
ϕ
b) 2π
radians
8
d) 180π radians
e) π radians
62.
r
a) 5π
 1
 22  =
 2
61
l
The radian measure of the angle at the
center of circle of radius 12cm which cuts
off an arc 18cm long.
a)
b)
c)
d)
e)
radians
r
5π
radians =
4
a)
b)
c)
d)
e)
65.
60.
With usual notations, θ = _______
67.
4
to degree
3π
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The length of the arc cut off on a circle of
radius 6cm by a central angle of 2π 3
radians
a)
b)
c)
d)
e)
12.566cm
10.033cm
12.113cm
9.156cm
6.56cm
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MCQs – Ch # 9: F.Sc Part 1
68.
80o =
5π
radians
6
4π
radians
b)
9
8
73.
If the measure of two angles of a ∆ABC is
o
30 and 70o then the 3rd angle is
a)
c)
A
π
radians
4
d) 180π radians
e) π radians
B
a)
b)
c)
d)
e)
69.
The radius of the circle when l = 3cm, θ =
3.4 radians.
a)
b)
c)
d)
e)
0.214 cm
9.419 cm
3.146 cm
4.978 cm
None of these
b) 4π
6
radians
a)
b)
c)
d)
e)
75.
In the second quadrant Sinθ is ________
a)
b)
c)
d)
e)
a) π
12
radians
b) π radians
8
π
radians
c)
8
d) π radians
e) 2 π radians
Written by NAUMAN IDREES ([email protected])
Perpendicular
?
Sinθ =
76.
In 15 minutes, the minutes hand of a clock
turns through
positive
negative
both
not defined
none of these
72.
In one hour, the hours hand of a clock
turns through
360o
180o
90o
60o
30o
a) base
b) hypotenuse
c) cos θ
d) tan θ
e) none of these
radians
9
c) π radians
4
d) 180π radians
e) 2 π radians
71.
30o
70o
80o
100o
210o
74.
In one hour, the minutes hand of a clock
turns through
70.
In one hour, the minutes hand of a clock
turns through
a) 5π
C
a)
b)
c)
d)
e)
77.
360o
180o
90o
60o
30o
Cosθ =
1
?
a) sin θ
b) tan θ
c) cos θ
d) sec θ
e) none of these
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MCQs – Ch # 9: F.Sc Part 1
78.
In the 2nd quadrant Sec θ is ________?
a)
b)
c)
d)
e)
79.
81.
82.
85.
positive
negative
both
not defined
<1
86.
3
2
1
0.5
None of these
88.
positive
negative
both
not defined
None of these
83.
Two cities whose longitudes are 30 E and
o
40 W on the equator are apart
1000 km
2000 km
2500 km
3351 km
7819.09 km
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A railway train is running on a circular
track of radius 500 meters at the rate of 30
km per hour, it will turn in 10 seconds
through an angle.
The pendulum of a clock is 30 cm long
and it swings through an angle of 30o each
second. How far does the tip of the
pendulum move in 1 second.
a)
b)
c)
d)
e)
o
a)
b)
c)
d)
e)
positive
negative
both
0
None of these
a) 4 46′28′′
b) 9 32′57 ′′
c) 18 46′28′′
d) 30o
e) 60o
In the 3rd quadrant Sin θ is _______ ?
a)
b)
c)
d)
e)
1000 km
2000 km
2500 km
3351 km
6702 km
In the 3rd quadrant Cosec θ is _________ ?
a)
b)
c)
d)
e)
87.
1
?
Two cities whose longitudes are 10oE and
20oW on the equator are apart.
a)
b)
c)
d)
e)
7.5o
15o
30o
60o
120o
The radian measure of the central angle of
an arc 50cm log on a circle of radius 25m
is
a)
b)
c)
d)
e)
Co sec θ =
a) cot θ
b) tan θ
c) sin θ
d) sec2 θ
e) 1 – sin θ
In 15 minutes the hours hand of a clock
turns through
a)
b)
c)
d)
e)
84.
positive
negative
both
not defined
–1
In the 2nd quadrant Cot θ is _______ ?
a)
b)
c)
d)
e)
80.
9
89.
10 cm
15.71 cm
20.94 cm
28.65 cm
40 cm
A railway train is running on a circular
track of radius 1000 meters at the rate of
30 km per hour, it will turn in 10 seconds
through an angle
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MCQs – Ch # 9: F.Sc Part 1
10
a) 4 46′28′′
b) 9 32′57 ′′
c) 18 46′28′′
d) 30o
e) 60o
1
rθ
2
d) r 2θ
e) rθ 2
c)
95.
90.
The pendulum of a clock is 40cm long and
it swings through an angle of 30o each
second. How far does the tip of the
pendulum move in 1 seconds?
a)
b)
c)
d)
e)
10cm
15.71cm
20.94cm
28.65cm
40cm
91. In the fourth quadrant Cosec θ is _______?
a)
b)
c)
d)
e)
92.
a)
b)
c)
d)
e)
93.
d)
e)
96.
positive
negative
both
0
None of these
A circular wire of radius 2cm is cut
straightened and then bent so as to lie
along the circumference of a hoop of
radius 24cm. the measure of the angle
subtended at the center of the hoop is
b)
c)
6
π
3
m2
m2
π
2
π
3
π
m2
m2
m2
6
d) 2m2
e) 1m2
97.
15o
30o
25o
60o
90o
–1
cosec θ
tan θ
1
– 11
π
The area of a sector with a central angle of
0.5 radians in a circular region whose
radius is 2m is
a)
An arc AB of length 5cm is marked on a
circle of radius 3cm. the area of the sector
bounded by this arc and the radii from A
and B is
a)
b)
c)
d)
e)
sec2 θ - tan2 θ = _______
a)
b)
c)
d)
e)
The area of a sector with a central angle of
1 radian in a circular region whose radius
is 2m.
a) 2m2
b) 1m2
c) 0.5m2
98.
7.5 cm2
7.5 m2
75 m2
75 cm2
None of these
cos 2
θ
2
+ sin 2
θ
2
= _________
1
4
1
b)
2
c) 2
d) 0
e) 1
a)
94.
The area of a sector of a circular region of
radius r and the central angle of the sector
θ radians is
1
a) rθ 2
2
1
b) r 2θ
2
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MCQs – Ch # 9: F.Sc Part 1
99.
In which quadrant does the terminal side
lie if sin θ > 0 and tan θ _______ ?
105.
− 3π
Cos
= _______ ?
2
106.
a)
b)
c)
d)
e)
1
0
–1
10
None of these
1
0
–1
10
None of these
Cosec2 θ - Cot2 θ = _______ ?
a)
b)
c)
d)
e)
− 3π
= _______ ?
2
1
0
–1
11
None of these
a)
b)
c)
d)
e)
102.
104.
1 – cos2 θ
1 – tan2 θ
1 + tan2 θ
1 – cot2 θ
1 + cot2 θ
Sin
Cos 9π = _______ ?
a)
b)
c)
d)
e)
sec2 θ = …………..
a)
b)
c)
d)
e)
101.
103.
1st
2nd
3rd
4th
None of these
a)
b)
c)
d)
e)
100.
11
1
0
–1
Tan2 θ
Sec2 θ
Cos22 θ = _______ ?
a)
b)
c)
d)
e)
1 – sin2 θ
1 + sin2 θ
1 – sin22 θ
1 - sin θ
1 + sin θ
1 + cot22 θ = _________ ?
a)
b)
c)
d)
e)
sec2 θ
cosec2 θ
cosec22 θ
sec2 θ
none of these
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([email protected])
FSc (Session: 2007-09)
ICMS College System Hayatabad, Peshawar
Written by NAUMAN IDREES ([email protected])
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